x +  y +  z =  0     (1)  
2x + 3y + 2z = -3     (2)
-x - 2y -  z =  1     (3)


Add equations (1) and (3). You will get

0*x - y  + 0*z = 1,     or simply   -y = 1,  which gives you  y = -1.

So, one unknown is just found: y = -1.

Substitute the found value of y into equation (1) and (2). You will get the system of 2 equations in 2 unknowns.


I hope you can easily solve it, since it is much easier than 3x3-system.